Subgroups — #44535260

Order 31347.

578 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782849	C₃	1	1	yes	maximal, characteristic, complemented
2	#23782844	C₃	1	2	yes	maximal, complemented
3	#23782841	C₃	1	2	yes	maximal, complemented
4	#23782841	C₃	1	2	yes	maximal, complemented
5	#23782837	C₃	1	2	yes	maximal, complemented
6	#23782836	C₃	1	2	yes	maximal, complemented
7	#23782834	C₃	1	1	yes	maximal, characteristic, complemented
8	#23782833	C₃	1	2	yes	maximal, complemented
9	#23782832	C₃	1	2	yes	maximal, complemented
10	#23782829	C₃	1	2	yes	maximal, complemented
11	#23782828	C₃	1	2	yes	maximal, complemented
12	#23782827	C₃	1	1	yes	maximal, characteristic, complemented
13	#23782826	C₃	1	2	yes	maximal, complemented
14	#23782823	C₃	1	1	yes	maximal, characteristic, complemented
15	#23782821	C₃	1	2	yes	maximal, complemented
16	#23782816	C₃	1	2	yes	maximal, complemented
17	#23782814	C₃	1	2	yes	maximal, complemented
18	#23782814	C₃	1	2	yes	maximal, complemented
19	#23782811	C₃	1	1	yes	maximal, characteristic, complemented
20	#23782810	C₃	1	2	yes	maximal, complemented
21	#23782807	C₃	1	1	yes	maximal, characteristic
22	#23782802	C₃	1	1	yes	maximal, characteristic
23	#23782801	C₃	1	2	yes	maximal
24	C₄₃×#6895	C₃	1	1	yes	maximal, characteristic, complemented
25	C₃×#11923958	C₃²	1	2	yes	—
26	C₃×#11923957	C₃²	1	2	yes	—
27	C₃×#11923957	C₃²	1	1	yes	characteristic
28	C₃×#11923957	C₃²	1	2	yes	—
29	C₃×#11923957	C₃²	1	1	yes	characteristic
30	C₃×#11923956	C₃²	1	2	yes	—
31	C₃×#11923956	C₃²	1	1	yes	characteristic
32	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
33	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	—
34	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
35	#16812500	C₃²	1	1	yes	characteristic
36	#16812500	C₃²	1	2	yes	—
37	#16812500	C₃²	1	2	yes	—
38	#16812500	C₃²	1	1	yes	characteristic
39	#16812500	C₃²	1	2	yes	—
40	#16812500	C₃²	1	2	yes	—
41	#16812500	C₃²	1	2	yes	—
42	#16812499	C₃²	1	2	yes	—
43	#16812499	C₃²	1	1	yes	characteristic
44	#16812499	C₃²	1	1	yes	characteristic
45	#16812499	C₃²	1	2	yes	—
46	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
47	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
48	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
49	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
50	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
51	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
52	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
53	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
54	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
55	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
56	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
57	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
58	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
59	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
60	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
61	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
62	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
63	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
64	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
65	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
66	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
67	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
68	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
69	(C₄₃⋊C₉)⋊C₉	C₃²	1	2	yes	—
70	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	—
71	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
72	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
73	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	—
74	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
75	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
76	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
77	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
78	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
79	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
80	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
81	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
82	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
83	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
84	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
85	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
86	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
87	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
88	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
89	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
90	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
91	C₄₃×C₉⋊C₉	C₃²	1	2	yes	—
92	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
93	C₄₃×C₉⋊C₉	C₃²	1	2	yes	—
94	C₄₃×C₉⋊C₉	C₃²	1	2	yes	—
95	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
96	C₄₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
97	C₄₃×C₃²⋊C₉	C₃²	1	2	yes	—
98	C₄₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
99	C₃²×C₄₃⋊C₃	C₃³	1	2	yes	—
100	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
101	#11923958	—	9	2	no	—
102	#11923957	—	9	2	no	—
103	#11923957	—	9	1	no	—
104	#11923957	—	9	2	no	—
105	#11923957	—	9	1	no	—
106	#11923956	—	9	2	no	—
107	#11923956	—	9	1	no	—
108	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
109	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
110	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
111	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
112	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
113	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
114	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
115	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
116	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
117	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
118	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
119	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
120	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
121	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
122	C₉×C₄₃⋊C₃	—	9	1	no	—
123	C₉×C₄₃⋊C₃	—	9	2	no	—
124	C₃³×C₄₃	C₃³	1	1	yes	characteristic
125	C₃×C₉×C₄₃	—	9	1	no	—
126	C₃×C₉×C₄₃	C₃³	1	2	yes	—
127	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
128	C₃×C₉×C₄₃	C₃³	1	2	yes	—
129	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
130	C₃×C₉×C₄₃	C₃³	1	2	yes	—
131	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
132	C₃×C₉×C₄₃	C₃³	1	2	yes	—
133	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
134	#10624914	—	43	1	no	maximal, Sylow
135	C₃²×C₄₃	—	3	1	no	—
136	C₃²×C₄₃	—	3	1	no	—
137	C₃²×C₄₃	—	3	2	no	—
138	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
139	C₃×C₄₃⋊C₃	—	3	1	no	—
140	C₃×C₄₃⋊C₃	—	3	2	no	—
141	C₃×C₄₃⋊C₃	—	3	2	no	—
142	C₃×C₄₃⋊C₃	—	3	2	no	—
143	C₃×C₄₃⋊C₃	—	3	2	no	—
144	C₃×C₄₃⋊C₃	—	3	2	no	—
145	C₃×C₄₃⋊C₃	—	3	1	no	—
146	C₉×C₄₃	—	3	2	no	—
147	C₉×C₄₃	—	3	1	no	—
148	C₉×C₄₃	—	3	2	no	—
149	C₉×C₄₃	—	3	1	no	—
150	C₉×C₄₃	—	3	2	no	—
151	C₉×C₄₃	—	3	1	no	—
152	C₉×C₄₃	—	3	2	no	—
153	C₉×C₄₃	—	3	1	no	—
154	C₄₃⋊C₉	—	3	2	no	—
155	C₄₃⋊C₉	—	3	2	no	—
156	C₄₃⋊C₉	—	3	2	no	—
157	C₄₃⋊C₉	—	3	2	no	—
158	C₄₃⋊C₉	—	3	2	no	—
159	C₄₃⋊C₉	—	3	2	no	—
160	C₄₃⋊C₉	—	3	2	no	—
161	C₄₃⋊C₉	—	3	2	no	—
162	C₄₃⋊C₉	—	3	2	no	—
163	C₄₃⋊C₉	—	3	1	no	—
164	C₄₃⋊C₉	—	3	1	no	—
165	C₄₃⋊C₉	—	3	2	no	—
166	C₄₃⋊C₉	—	3	2	no	—
167	#6900	—	43	1	no	—
168	#6899	—	43	2	no	—
169	#6899	—	43	2	no	—
170	#6899	—	43	2	no	—
171	#6899	—	43	2	no	—
172	#6898	—	43	2	no	—
173	#6898	—	43	1	no	—
174	#6897	—	43	2	no	—
175	#6897	—	43	2	no	—
176	#6897	—	43	2	no	—
177	#6896	—	43	2	no	—
178	#6896	—	43	1	no	—
179	#6896	—	43	2	no	—
180	#6896	—	43	1	no	—
181	#6895	—	43	2	no	—
182	#6895	C₄₃⋊C₃	1	1	yes	characteristic, complemented
183	#6894	—	43	2	no	—
184	#6894	—	43	2	no	—
185	#6894	—	43	1	no	—
186	#6894	—	43	2	no	—
187	#6894	—	43	2	no	—
188	#6893	—	43	1	no	—
189	C₉⋊H(3,𝔽₃)	—	43	1	no	—
190	C₉⋊H(3,𝔽₃)	—	43	2	no	—
191	C₃×C₄₃	—	9	1	no	—
192	C₃×C₄₃	3₋¹⁺⁴	1	2	yes	—
193	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
194	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
195	C₄₃⋊C₃	—	9	1	no	—
196	C₄₃⋊C₃	—	9	2	no	—
197	C₃×3₋¹⁺²	—	43	2	no	—
198	C₃×3₋¹⁺²	—	43	2	no	—
199	C₃×3₋¹⁺²	—	43	1	no	—
200	C₃×3₋¹⁺²	—	43	2	no	—
201	C₃×3₋¹⁺²	—	43	1	no	—
202	C₃×3₋¹⁺²	—	43	2	no	—
203	C₃×3₋¹⁺²	—	43	1	no	—
204	C₃×H(3,𝔽₃)	—	43	1	no	—
205	C₃²×C₉	—	43	2	no	—
206	C₃²×C₉	—	43	1	no	—
207	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
208	C₉⋊C₉	—	43	2	no	—
209	C₉⋊C₉	—	43	2	no	—
210	C₉⋊C₉	—	43	2	no	—
211	C₉⋊C₉	—	43	2	no	—
212	C₉⋊C₉	—	43	2	no	—
213	C₉⋊C₉	—	43	2	no	—
214	C₉⋊C₉	—	43	2	no	—
215	C₉⋊C₉	—	43	2	no	—
216	C₉⋊C₉	—	43	2	no	—
217	C₉⋊C₉	—	43	2	no	—
218	C₉⋊C₉	—	43	2	no	—
219	C₉⋊C₉	—	43	2	no	—
220	C₉⋊C₉	—	43	2	no	—
221	C₉⋊C₉	—	43	2	no	—
222	C₉⋊C₉	—	43	2	no	—
223	C₉⋊C₉	—	43	2	no	—
224	C₉⋊C₉	—	43	2	no	—
225	C₉⋊C₉	—	43	2	no	—
226	C₉⋊C₉	—	43	2	no	—
227	C₉⋊C₉	—	43	2	no	—
228	C₉⋊C₉	—	43	2	no	—
229	C₉⋊C₉	—	43	2	no	—
230	C₉⋊C₉	—	43	2	no	—
231	C₉⋊C₉	—	43	2	no	—
232	C₉⋊C₉	—	43	2	no	—
233	C₉⋊C₉	—	43	1	no	—
234	C₉⋊C₉	—	43	1	no	—
235	C₉⋊C₉	—	43	2	no	—
236	C₉⋊C₉	—	43	2	no	—
237	C₉⋊C₉	—	43	2	no	—
238	C₉⋊C₉	—	43	1	no	—
239	C₉⋊C₉	—	43	2	no	—
240	C₉⋊C₉	—	43	2	no	—
241	C₉⋊C₉	—	43	1	no	—
242	C₉⋊C₉	—	43	2	no	—
243	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
244	C₉⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
245	C₉⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
246	C₉⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
247	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
248	C₉⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
249	C₃²⋊C₉	—	43	2	no	—
250	C₃²⋊C₉	—	43	1	no	—
251	C₃²⋊C₉	—	43	1	no	—
252	C₃²⋊C₉	—	43	2	no	—
253	C₃²⋊C₉	—	43	2	no	—
254	C₃²⋊C₉	—	43	2	no	—
255	C₃²⋊C₉	—	43	2	no	—
256	C₃²⋊C₉	—	43	2	no	—
257	C₃²⋊C₉	—	43	2	no	—
258	C₃²⋊C₉	—	43	2	no	—
259	C₃²⋊C₉	—	43	2	no	—
260	C₃²⋊C₉	—	43	2	no	—
261	C₃²⋊C₉	—	43	2	no	—
262	C₃²⋊C₉	—	43	2	no	—
263	C₃²⋊C₉	—	43	2	no	—
264	C₃²⋊C₉	—	43	2	no	—
265	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
266	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
267	C₉²	—	43	1	no	—
268	C₉²	—	43	2	no	—
269	C₉²	—	43	2	no	—
270	C₉²	—	43	1	no	—
271	C₄₃	#10624914	1	1	yes	characteristic, complemented, Sylow
272	C₃³	—	43	2	no	—
273	C₃³	—	43	1	no	—
274	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
275	3₋¹⁺²	—	387	2	no	—
276	3₋¹⁺²	—	387	1	no	—
277	3₋¹⁺²	—	387	2	no	—
278	3₋¹⁺²	—	387	1	no	—
279	3₋¹⁺²	—	387	2	no	—
280	3₋¹⁺²	—	387	1	no	—
281	3₋¹⁺²	—	387	2	no	—
282	H(3,𝔽₃)	—	387	1	no	—
283	C₃×C₉	—	9	1	no	—
284	C₃×C₉	—	43	2	no	—
285	C₃×C₉	—	43	2	no	—
286	C₃×C₉	—	43	2	no	—
287	C₃×C₉	—	43	2	no	—
288	C₃×C₉	—	43	2	no	—
289	C₃×C₉	—	43	2	no	—
290	C₃×C₉	—	43	1	no	—
291	C₃×C₉	—	43	2	no	—
292	C₃×C₉	—	43	2	no	—
293	C₃×C₉	—	43	1	no	—
294	C₃×C₉	—	43	2	no	—
295	C₃×C₉	—	43	2	no	—
296	C₃×C₉	—	43	2	no	—
297	C₃×C₉	—	387	2	no	—
298	C₃×C₉	—	387	1	no	—
299	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
300	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
301	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
302	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
303	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
304	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
305	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
306	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
307	C₃²	—	3	2	no	—
308	C₃²	—	3	1	no	—
309	C₃²	—	3	1	no	—
310	C₃²	—	129	2	no	—
311	C₃²	—	129	2	no	—
312	C₃²	—	129	2	no	—
313	C₃²	—	129	1	no	—
314	C₃²	—	129	2	no	—
315	C₃²	—	129	2	no	—
316	C₃²	—	129	1	no	—
317	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
318	C₉	—	3	2	no	—
319	C₉	—	3	2	no	—
320	C₉	—	3	2	no	—
321	C₉	—	3	1	no	—
322	C₉	—	3	1	no	—
323	C₉	—	3	1	no	—
324	C₉	—	3	2	no	—
325	C₉	—	3	1	no	—
326	C₉	—	129	2	no	—
327	C₉	—	129	2	no	—
328	C₉	—	129	2	no	—
329	C₉	—	129	2	no	—
330	C₉	—	129	2	no	—
331	C₉	—	129	2	no	—
332	C₉	—	129	2	no	—
333	C₉	—	129	2	no	—
334	C₉	—	129	2	no	—
335	C₉	—	129	2	no	—
336	C₉	—	129	2	no	—
337	C₉	—	129	1	no	—
338	C₉	—	129	1	no	—
339	C₃	—	9	1	no	—
340	C₃	—	387	2	no	—
341	C₃	—	387	1	no	—
342	C₃	#23782921	1	2	yes	—
343	C₃	#23782922	1	1	yes	characteristic
344	C₃	#23782923	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Fitting	C₄₃×#6895	C₃
prime radical	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²
hypercenter	#6895	C₄₃⋊C₃
hypocenter	C₄₃	#10624914
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ #6895

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #23782849	C₃	semidirect
2. #23782844	C₃	semidirect
3. #23782841	C₃	semidirect
4. #23782841	C₃	semidirect
5. #23782837	C₃	semidirect
6. #23782836	C₃	semidirect
7. #23782834	C₃	semidirect
8. #23782833	C₃	semidirect
9. #23782832	C₃	semidirect
10. #23782829	C₃	semidirect
11. #23782828	C₃	semidirect
12. #23782827	C₃	semidirect
13. #23782826	C₃	semidirect
14. #23782823	C₃	semidirect
15. #23782821	C₃	semidirect
16. #23782816	C₃	semidirect
17. #23782814	C₃	semidirect
18. #23782814	C₃	semidirect
19. #23782811	C₃	semidirect
20. #23782810	C₃	semidirect
24. C₄₃×#6895	C₃	semidirect
182. #6895	C₄₃⋊C₃	semidirect
271. C₄₃	#10624914	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23782849	3
#23782844	3
#23782841	3
#23782837	3
#23782836	3
#23782834	3
#23782833	3
#23782832	3
#23782829	3
#23782828	3
#23782827	3
#23782826	3
#23782823	3
#23782821	3
#23782816	3
#23782814	3
#23782811	3
#23782810	3
#23782807	3
#23782802	3
#23782801	3
C₄₃×#6895	3
#10624914	43